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Abstract

Disclosed is a technique for using the vector processing facility of a large mainframe to quickly and efficiently alter the sampling rate of a waveform.

Country

United States

Language

English (United States)

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Vector Processor Method for Waveform-Sampling Rate Change

Disclosed is a technique for using the vector processing facility of a large
mainframe to quickly and efficiently alter the sampling rate of a waveform.

To change the sampling rate of a waveform by a factor of n/m, one must pad
each sample of the waveform with n-1 zeros, low-pass filter the padded
waveform with a filter of cutoff frequency 3.14159/n (interpolation), and select
every mth point [1] (decimation). When m and n are not small integers, the
above technique can result in a substantial amount of computation. Computation
can be saved by observing that most of the waveform to be filtered consists of
zeroes, but only at the expense of program complexity. This disclosure
describes an efficient technique for sampling rate changes that utilizes the 3090
vector processor with minimal program complexity.

Let x denote the signal whose sampling rate is to be changed.
Define z as

x(i) if j = ni

z(j) =

0 otherwise

Define y as the interpolated version of x, and h the low-pass
filter. Then,
y(k) = S z(j)h(k - j)

j

z only contributes to the above convolution for j = n*i. One
may then write
y(k) = S z(ni)h(k - ni)

i

Let k = 1 * n + p, p < n - 1. Then
y(ln + p) = S z(ni)h(ln + p - ni)

i

Define

yp(l) = y(ln + p)

hp(l) = h(ln + p)

Then

yp(l) = S x(i)hp(l - i)

i
where we have substituted x for z as per the original
definition.

The above equation says that we can produce y from x by dividing h into n
filters, using each of these shorter sequences to filter y and then to merge the
filtered sequences together. This operation can be done efficiently using the
ESSL routine SCON [2] which implements FIR filtering with multiple filters using
the vector processor. In particular, by correctly...